The aircraft will be used for pilot and maintainer training for the UK team currently based in the USA. At Eglin, pilots from the Royal Navy and RAF and ground crew are working alongside their US Marine Corps colleagues learning all they can about maintaining the aircraft and how to fly the platforms to get the best out of them.
Group Captain Harv Smyth, the UKs Joint Strike Fighter National Deputy, said:

Todays arrival of BK-3 is the latest step in delivering the F-35s unprecedented capability to UK Defence.
With each passing day our Lightning II programme is maturing. In less than a year we have taken ownership of our first 3 aircraft and begun both pilot and engineer training.
The Lightning II truly represents a turning point for the UKs combat air capability and will dramatically increase our ability to defend national sovereignty interests and ensure security around the globe.
​

The F-35 Lightning II is a fifth-generation fighter, combining advanced stealth with fighter speed and agility. More than 500 British suppliers will build 15% of each F-35 produced.
UK industry is responsible for numerous F-35 components including the aft fuselage, fuel system and crew escape system.

Hopefully an adult can answer but why are Ryan Air Force involved with this carrier aircraft?

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If "Joint" Force Lightning goes anything like "Joint" Force Harrier then the RAF will end up footing 75% of the manning bill, all of the real estate and supporting functions, and most of the training (stand fast the two instructors the RN used to wheel out for the cameras at every available opportunity).